Surface Finish Quality

Surface Finish Quality Experiment Report

Naser Alkhdour Timothy Ehiabor Stephen Noronha

For IEE 572: Design of Experiment Professor: Dr. D. C. Montgomery Industrial & Management Systems Engineering Dept. Arizona State University Tempe, AZ 85281 December 4, 2000 Table of Content

Problem Statement…………………………….…….3 Factors of Interest…………………………….……..3 Choice of Experimental Design……………….…….3 Surface Finish Design Outlook……………….……..4 Performing the Experiment……………………….…5 Statistical Analysis of Data………………………….5 Conclusions and Recommendations………………....5 Appendix A……………………………………...…...6 Appendix B…………………………………………15 Works Cited………………………………………....22

2 Problem statement

Mill machines are used to cut and finish surfaces. Finding a set of conditions for cutting the smoothest surface over a given experimental space using the manufacturing lab mill machine would appear to be of some interest as a process improvement problem. Specifically, plastic wafers would be used in the milling process. Their surfaces would be cut flat and finished by the mill process. The degree of smoothness or quality of finish (response variable) obtained can then be measured using a roughness measurement gauge (Profilometer).

Objective:

The objective of this experiment is to learn how each of the factors listed below affects surface finish of a plastic wafer, also to determine how the factors interact with one another.

Factors of interest

1) Step-over size (0.25in to 0.50in) – how far the cutting point moves following each cut—factor A. 2) Depth of cut: (0.05in to 0.25in)—factor B. 3) Feed rate (10in/min to 40in/min)—factor C. 4) The spindle speed (1000-2500 rpm)—factor D. 5) Cutting pattern (zigzag or concentric)—factor E.

Of the factors with ranking in order of importance, (1=most likely to affect smoothness; 5= least likely to affect smoothness), it is tentatively suggested that two levels of each factor be chosen, thus facilitating a 25-1 fractional factorial design. The levels over which the factors were determined and ranking order used were based on advice from expert knowledge of the lab personnel.

Choice of Experimental Design

This experiment is an example of a 2k-p design with k=5 and p=1. This is a one-half of the full 25 (32) design points. The reason for the reduction from the full design points is due to cost of material and limited time period. The sample size decided on for this experiment is one (n=1). That is, this is an unreplicated 25-1 fractional factorial design because the number of factors under consideration is large enough (five factors). The run order and specimen specification for the experiment is shown in the figure and the table on next page. This is the run order generated by Design Expert. In this Design Expert output, there are two blocks, each block represent one day. In other words, we are blocking the experiment by day. This is to minimize the variability effect as a result of nuisance factor i.e. the different level of daily usage of the milling machine.

3 Surface Finish Quality Experiment: Design Outlook

Depths of cut =0.05in & .25in To be used: 1. 2 flutes 2. ½ ” cutter diameter

STD RUN Block Step- depth of Feed spindle cutting Response over cut(in) rate(in/min) speed (rpm) pattern (smoothness) size(in) 10 1 Block 1 0.5 0.05 10 2500 zigzag 38 2 2 Block 1 0.5 0.05 10 1000 concentric 56 3 3 Block 1 0.25 0.25 10 1000 concentric 102 11 4 Block 1 0.25 0.25 10 2500 zigzag 60 6 5 Block 1 0.5 0.05 40 1000 zigzag 279 7 6 Block 1 0.25 0.25 40 1000 zigzag 222.5 15 7 Block 1 0.25 0.25 40 2500 concentric 156 14 8 Block 1 0.5 0.05 40 2500 concentric 117.5 4 9 Block 2 0.5 0.25 10 1000 zigzag 136.5 12 10 Block 2 0.5 0.25 10 2500 concentric 49.5 13 11 Block 2 0.25 0.05 40 2500 zigzag 87.5 16 12 Block 2 0.5 0.25 40 2500 zigzag 199 5 13 Block 2 0.25 0.05 40 1000 concentric 212.5 1 14 Block 2 0.25 0.05 10 1000 zigzag 45 9 15 Block 2 0.25 0.05 10 2500 concentric 32.5 8 16 Block 2 0.5 0.25 40 1000 concentric 248.5 Table showing run order, varying factors and responses.

4 Performing the Experiment:

After setting up the experiment using Design expert, we conducted the experiment using the factors as indicted in the Table above. Over the span of 2 days to avoid the problem of nuisance factors such as the warm-up effect, as a result of prolonged use of the Mill machine by other students before us. This experiment was conducted with a ½  diameter cutter having 2 flutes (cutting edges). The cutting pattern was generated on SmartCam. Care was taken to use the coolant in order to avoid the Warping and removal of heat from the material as the cutting process was carried out. The instrument that was used to measure the smoothness of the surface was Surface Tester (Profilometer). The instrument was calibrated so as to avoid errors in the reading. After calibration, the samples were measured for smoothness at 2 different locations. The average of the readings was used as the response value in the experiment.

Statistical Analysis of the Data:

Appendix A shows the ANOVA table and other Design Expert analysis output for the selected 25-1 Resolution V, fractional factorial Model. As shown from the Normal plot of effects, only main factors C & D are significant with a very mild CD interaction effect. There is no three-factor or higher order interaction effect. Therefore, we feel confident to say that only C, D and CD are important effects. And the SSMODEL of 86306.38 accounts for 85% of the total variability in the smoothness. The model’s F-statistic, which test simultaneously if C, D and CD (interaction) are significant, has a value of 20.47—this is significant. Furthermore, observation of the residual’s normal probability plot and the other plots of residuals seems to support our claims in the paragraph above. For example, the normal probability plot easily passed the “fat-pencil test” and the plots of residuals versus run order, expected values and other parameters did not reveal any serious abnormality. All the factors have positive effect; however, factor C, has a much higher effect than D and the CD interaction. A plot of the feed rate (C) and spindle speed (D) interaction shows that the best surface finish is achieved at a low-level feed rate and high-level spindle speed. The three-dimensional surface and contour plots also show that the direction for further optimization experiment will be in that of steepest decent of the surface slopes or the direction of the smallest values of the contour plot. This is because the smaller the response values, the better surface finish (smoothness). Since this experiment was conducted in blocks, we conducted a comparison between blocks with the hypothesis, Ho: j = 0, using the ratio:

SSBLOCK /MSE = 25/1405.58 = 0.018

This showed that the effect of blocking variable (days) is not significant. In other words, there are no added variability introduced into the experiment mainly as a result of the fact that the experiment was conducted in two different days (blocks). It would have been ok if we had performed the 16 runs in one day instead of two but our choice of two days (blocks) was to guide against any warm-up effect as a result of prolonged use of the Mill machine by other students before us. Because only two factors were found to be

5 significant, the 25-1 fractional factorial design can be collapsed into a full 22 factorial design replicated four (4) times. See Appendix B for the analysis of the resulting 22 factorial design (with 4 replicates). The results shown in Appendix B confirmed the Appendix A analysis described above. There is no significant difference between results from Appendix A and that from Appendix B. The model equation for this experiment is shown below:

Y = 0 + 3X3 + 4X4 + 34X3X4 + 

In terms of coded value:

Y = 127.63 + 62.67*C – 35.13*D – 15.19*C*D

In terms of actual factors:

Y = 46.042 + 6.54*Feedrate – 0.013*Spindle speed – 0.00135*Feed rate*Spindle speed

This model equation can be used to predict design points. This test is often necessary in order to see how well the model equation can correctly describe the experiment.

Conclusions and Recommendations:

The practical conclusions from this experiment are that only 2 factors Feed rate and Spindle speed, contribute to the smoothness of the Plastic material. Because of mild interaction between the 2 factors (feedrate and spindle speed), the best surface finish can be achieved by a combination of low-level feed rate and a high-level spindle speed. From the rank order that we gave earlier (page 3) we suspected that step-over size (factor 1 or A) might contribute rather significantly to the smoothness of the material. However, data analysis showed otherwise and the reason for this is because we have not varied the factor (step-over size) over a wide enough range. We therefore recommend that further experimentation to includes the three factors: A, C and D; with factor A varied over a wider range (0.25in to 1.00in)—just to be sure about the contribution of step-over size to the level of surface finish of plastic materials. We could not do this (factor A) confirmation testing because of cost and time constraints. The direction for optimization experiment will be in that of steepest decent of the surface slopes or the direction of the smallest values of the contour plot. This is because the smaller the response values; the better surface finishes (smoothness). See 3D and contour interaction plots on Appendix A (pages 13 & 14).

6 Appendix A:

STD RUN Block Step- depth of Feed spindle cutting Response over cut(in) rate(in/min) speed (rpm) pattern (smoothness) size(in) 10 1 Block 1 0.5 0.05 10 2500 zigzag 38 2 2 Block 1 0.5 0.05 10 1000 concentric 56 3 3 Block 1 0.25 0.25 10 1000 concentric 102 11 4 Block 1 0.25 0.25 10 2500 zigzag 60 6 5 Block 1 0.5 0.05 40 1000 zigzag 279 7 6 Block 1 0.25 0.25 40 1000 zigzag 222.5 15 7 Block 1 0.25 0.25 40 2500 concentric 156 14 8 Block 1 0.5 0.05 40 2500 concentric 117.5 4 9 Block 2 0.5 0.25 10 1000 zigzag 136.5 12 10 Block 2 0.5 0.25 10 2500 concentric 49.5 13 11 Block 2 0.25 0.05 40 2500 zigzag 87.5 16 12 Block 2 0.5 0.25 40 2500 zigzag 199 5 13 Block 2 0.25 0.05 40 1000 concentric 212.5 1 14 Block 2 0.25 0.05 10 1000 zigzag 45 9 15 Block 2 0.25 0.05 10 2500 concentric 32.5 8 16 Block 2 0.5 0.25 40 1000 concentric 248.5 Table showing run order, varying factors and responses.

DESIGN-EXPERT Plot sm othness N o rm a l p lo t

A: Step over size B: Depth of cut 9 9 C: Feed rate D: Spindle speed C

y 9 5 t

E: cutting pattern i l

i 9 0 b

a 8 0 b

o 7 0 r p 5 0 %

m 2 0 r

N C D 5 D 1

-7 0 .2 5 -2 1 . 3 4 2 7 .5 6 7 6 .4 7 1 2 5 .3 8

E ffe c t

7 Use your mouse to right click on individual cells for definitions. Response: smothness ANOVA for Selected Factorial Model Analysis of variance table [Partial sum of squares] Sum of Mean F Source Squares DF Square Value Prob > F Block 25.00 1 25.00 Model 86306.38 3 28768.79 20.47 < 0.0001 significant C 62875.56 1 62875.56 44.73 < 0.0001 D 19740.25 1 19740.25 14.04 0.0032 CD 3690.56 1 3690.56 2.63 0.1334 Residual 15461.38 11 1405.58 Cor Total 1.018E+005 15

The Model F-value of 20.47 implies the model is significant. There is only a 0.01% chance that a "Model F-Value" this large could occur due to noise.

Values of "Prob > F" less than 0.0500 indicate model terms are significant. In this case C, D are significant model terms. Values greater than 0.1000 indicate the model terms are not significant. If there are many insignificant model terms (not counting those required to support hierarchy), model reduction may improve your model.

Std. Dev. 37.49 R-Squared 0.8481 Mean 127.63 Adj R-Squared 0.8066 C.V. 29.38 Pred R-Squared 0.6786 PRESS 32711.67 Adeq Precision 9.453

The "Pred R-Squared" of 0.6786 is in reasonable agreement with the "Adj R-Squared" of 0.8066.

"Adeq Precision" measures the signal to noise ratio. A ratio greater than 4 is desirable. Your ratio of 9.453 indicates an adequate signal. This model can be used to navigate the design space.

Coefficient Standard 95% CI 95% CI Factor Estimate DF Error Low High VIF Intercept 127.63 1 9.37 107.00 148.25 Block 1 1.25 1 Block 2 -1.25 C-Feed rate 62.69 1 9.37 42.06 83.32 1.00 D-Spindle speed -35.13 1 9.37 -55.75 -14.50 1.00 CD -15.19 1 9.37 -35.82 5.44 1.00

8 Final Equation in Terms of Coded Factors:

smothness = +127.63 +62.69 * C -35.13 * D -15.19 * C * D

Final Equation in Terms of Actual Factors:

smothness = +46.04167 +6.54167 * Feed rate -0.013083 * Spindle speed -1.35000E-003 * Feed rate * Spindle speed

Diagnostics Case Statistics StandardActual Predicted StudentCook's Outlier Run Order Value Value Residual LeverageResidual Distance t Order 1 45.00 83.62 -38.62 0.313 -1.243 0.140 -1.278 14 2 56.00 86.12 -30.12 0.313 -0.969 0.085 -0.966 2 3 102.00 86.12 15.88 0.313 0.511 0.024 0.493 3 4 136.50 83.62 52.88 0.313 1.701 0.263 1.889 9 5 212.50 239.38 -26.88 0.313 -0.865 0.068 -0.854 13 6 279.00 241.88 37.13 0.313 1.194 0.130 1.221 5 7 222.50 241.88 -19.38 0.313 -0.623 0.035 -0.605 6 8 248.50 239.38 9.13 0.313 0.294 0.008 0.281 16 9 32.50 43.75 -11.25 0.313 -0.362 0.012 -0.347 15 10 38.00 46.25 -8.25 0.313 -0.265 0.006 -0.254 1 11 60.00 46.25 13.75 0.313 0.442 0.018 0.426 4 12 49.50 43.75 5.75 0.313 0.185 0.003 0.177 10 13 87.50 138.75 -51.25 0.313 -1.649 0.247 -1.812 11 14 117.50 141.25 -23.75 0.313 -0.764 0.053 -0.749 8 15 156.00 141.25 14.75 0.313 0.474 0.020 0.457 7 16 199.00 138.75 60.25 0.313 1.938 0.342 2.277 12 Note: Predicted values include block corrections.

Proceed to Diagnostic Plots (the next icon in progression). Be sure to look at the: 1) Normal probability plot of the studentized residuals to check for normality of residuals. 2) Studentized residuals versus predicted values to check for constant error. 3) Outlier t versus run order to look for outliers, i.e., influential values. 4) Box-Cox plot for power transformations.

If all the model statistics and diagnostic plots are OK, finish up with the Model Graphs icon.

9 DESIGN-EXPERT Plot sm othness N o rm a l p lo t o f re s id ua ls

t 9 0 i l i

b 8 0 a

b 7 0 o r p

m 2 0 r o

N 1 0 5

-5 1 . 2 5 -2 3 . 3 7 5 4 .5 3 2 .3 7 5 6 0 . 2 5

R e s id u a l

DESIGN-EXPERT Plot sm othness R e s id ua ls vs . P re d ic te d 6 0 . 2 5

3 2 . 3 7 5 s l a u d

i 4 . 5 s e R

-2 3 . 3 7 5

-5 1 . 2 5

4 3 .7 5 9 3 .2 8 1 4 2 . 8 1 1 9 2 .3 4 2 4 1 . 8 8

P re d i c te d

10 DESIGN-EXPERT Plot sm othness R e s id ua ls vs . R un 6 0 . 2 5

3 2 . 3 7 5 s l a u d

i 4 . 5 s e R

-2 3 . 3 7 5

-5 1 . 2 5

1 4 7 1 0 1 3 1 6

R u n N u m b e r

DESIGN-EXPERT Plot sm othness R e s id ua ls vs . F e e d ra te 6 0 . 2 5

3 2 . 3 7 5 s l a u d

i 4 . 5 s e R

-2 3 . 3 7 5

-5 1 . 2 5

1 0 1 5 2 0 2 5 3 0 3 5 4 0

F e e d ra te

11 DESIGN-EXPERT Plot sm othness R e s id ua ls vs . S p ind le s p e e d 6 0 . 2 5

3 2 . 3 7 5 s l a u d

i 4 . 5 s e R

-2 3 . 3 7 5

-5 1 . 2 5

1 0 0 0 1 2 5 0 1 5 0 0 1 7 5 0 2 0 0 0 2 2 5 0 2 5 0 0

S p in d l e s p e e d

DESIGN-EXPERT Plot sm othness O utlie r T 3 . 5 0

1 . 7 5 T

l 0 . 0 0 t u O

-1 . 7 5

-3 . 5 0

1 4 7 1 0 1 3 1 6

R u n N u m b e r

12 DESIGN-EXPERT Plot Inte ra c tio n G ra p h D : S p i n d l e s p e e d sm othness 2 7 9 X = C: Feed rate Y = D: Spindle speed

D- 1000.000 2 1 3 . 2 0 6 D+ 2500.000 Actual Factors

A: Step over size = 0.38 s s

B: Depth of cut = 0.15 e

E: cutting pattern = concentricn 1 4 7h . 4 1 3 t o m s

8 1 . 6 1 9 3

1 5 . 8 2 5 7

1 0 .0 0 1 7 .5 0 2 5 .0 0 3 2 . 5 0 4 0 . 0 0

C : F e e d ra te

DESIGN-EXPERT Plot sm othness X = C: Feed rate Y = D: Spindle speed

Actual Factors A: Step over size =2 40.38 0 .6 2 5 B: Depth of cut = 0.15 E: cutting pattern =1 9concentric 1 .7 1 9

1 4 2.8 1 3 s s

9 3 .9e 0 6 2 n h t 4 5 o m s

2 5 0 0 .0 0 4 0 .0 0 2 1 2 5 .0 0 3 2 .5 0 1 7 5 0 .0 0 2 5 .0 0 D : S p in d le s1 p 3 e 7 e5 .0 d 0 1 7 .5 0 C : F e e d ra te 1 0 0 0 .0 0 1 0 .0 0

13 DESIGN-EXPERT Plot s m o thne s s 2 5 0 0 .0 0 sm othness X = C: Feed rate Y = D: Spindle speed

Actual Factors A: Step over size = 0.382 1 2 5 .0 0 B: Depth of cut = 0.15 E: cutting pattern = concentricd e 7 7 .6 0 4 2 e p

s 1 1 0 .2 0 8 1 4 2 .8 1 3

e 1 7 5l 0 .0 0 d n i p S

: 1 7 5 .4 1 7 D

1 3 7 5 .0 0 2 0 8 .0 2 1

1 0 0 0 .0 0 1 0 .0 0 1 7 .5 0 2 5 .0 0 3 2 .5 0 4 0 .0 0

C : F e e d ra te

14 Appendix B:

Std Run Blocks feed rate spindle speed Response

6 1 Block 1 40.00 1000.00 279 7 2 Block 1 40.00 1000.00 222.5 9 3 Block 1 10.00 2500.00 38 8 4 Block 1 40.00 1000.00 212.5 5 5 Block 1 40.00 1000.00 248.5 4 6 Block 1 10.00 1000.00 56 11 7 Block 1 10.00 2500.00 60 15 8 Block 1 40.00 2500.00 156 13 9 Block 1 40.00 2500.00 117.5 3 10 Block 1 10.00 1000.00 102 12 11 Block 1 10.00 2500.00 49.5 2 12 Block 1 10.00 1000.00 136.5 10 13 Block 1 10.00 2500.00 32.5 16 14 Block 1 40.00 2500.00 87.5 1 15DESIGN-EXPERT Plot Block 1 10.00 1000.00 sm oothness N o rm a l p lo t 45 14 16A: Feed rate Block 1 40.00 2500.00 B: spindle speed 9 9 199 9 5 A

y 9 0 t i l i 8 0 b

a 7 0 b o r

l 3 0 a 2 0 m r

N A B 5 B 1

-7 0 . 2 5 -2 1 . 3 4 2 7 .5 6 7 6 . 4 7 1 2 5 . 3 7 15

E ffe c t Use your mouse to right click on individual cells for definitions. Response: smoothness ANOVA for Selected Factorial Model Analysis of variance table [Partial sum of squares] Sum of Mean F Source Squares DF Square Value Prob > F Model 86306.38 3 28768.79 22.29 < 0.0001 significant A 62875.56 1 62875.56 48.72 < 0.0001 B 19740.25 1 19740.25 15.30 0.0021 AB 3690.56 1 3690.56 2.86 0.1166 Pure Error 15486.38 12 1290.53 Cor Total 1.018E+005 15

The Model F-value of 22.29 implies the model is significant. There is only a 0.01% chance that a "Model F-Value" this large could occur due to noise.

Values of "Prob > F" less than 0.0500 indicate model terms are significant. In this case A, B are significant model terms. Values greater than 0.1000 indicate the model terms are not significant. If there are many insignificant model terms (not counting those required to support hierarchy), model reduction may improve your model.

Std. Dev. 35.92 R-Squared 0.8479 Mean 127.63 Adj R-Squared 0.8098 C.V. 28.15 Pred R-Squared 0.7295 PRESS 27531.33 Adeq Precision 10.891

The "Pred R-Squared" of 0.7295 is in reasonable agreement with the "Adj R-Squared" of 0.8098.

"Adeq Precision" measures the signal to noise ratio. A ratio greater than 4 is desirable. Your ratio of 10.891 indicates an adequate signal. This model can be used to navigate the design space.

16 Coefficient Standard 95% CI 95% CI Factor Estimate DF Error Low High VIF Intercept 127.63 1 8.98 108.06 147.19 A-Feed rate 62.69 1 8.98 43.12 82.26 1.00 B-spindle speed -35.13 1 8.98 -54.69 -15.56 1.00 AB -15.19 1 8.98 -34.76 4.38 1.00

Final Equation in Terms of Coded Factors:

smoothness = +127.63 +62.69 * A -35.13 * B -15.19 * A * B

Final Equation in Terms of Actual Factors:

smoothness = +46.04167 +6.54167 * Feed rate -0.013083 * spindle speed -1.35000E-003 * Feed rate * spindle speed

Diagnostics Case Statistics StandardActual Predicted StudentCook's Outlier Run Order Value Value Residual LeverageResidual Distance t Order 1 45.00 84.88 -39.88 0.250 -1.282 0.137 -1.321 15 2 136.50 84.88 51.63 0.250 1.659 0.229 1.810 12 3 102.00 84.88 17.13 0.250 0.550 0.025 0.534 10 4 56.00 84.88 -28.88 0.250 -0.928 0.072 -0.922 6 5 248.50 240.63 7.88 0.250 0.253 0.005 0.243 5 6 279.00 240.63 38.38 0.250 1.233 0.127 1.264 1 7 222.50 240.63 -18.13 0.250 -0.583 0.028 -0.566 2 8 212.50 240.63 -28.13 0.250 -0.904 0.068 -0.897 4 9 38.00 45.00 -7.00 0.250 -0.225 0.004 -0.216 3 10 32.50 45.00 -12.50 0.250 -0.402 0.013 -0.387 13 11 60.00 45.00 15.00 0.250 0.482 0.019 0.466 7 12 49.50 45.00 4.50 0.250 0.145 0.002 0.139 11 13 117.50 140.00 -22.50 0.250 -0.723 0.044 -0.708 9 14 199.00 140.00 59.00 0.250 1.896 0.300 2.170 16 15 156.00 140.00 16.00 0.250 0.514 0.022 0.498 8 16 87.50 140.00 -52.50 0.250 -1.688 0.237 -1.850 14

Proceed to Diagnostic Plots (the next icon in progression). Be sure to look at the: 1) Normal probability plot of the studentized residuals to check for normality of residuals. 2) Studentized residuals versus predicted values to check for constant error. 3) Outlier t versus run order to look for outliers, i.e., influential values.

17 4) Box-Cox plot for power transformations.

If all the model statistics and diagnostic plots are OK, finish up with the Model Graphs icon.

DESIGN-EXPERT Plot sm oothness N o rm a l p lo t o f re s id ua ls

t 9 0 i l i

b 8 0 a

b 7 0 o r p

m 2 0 r o

N 1 0 5

DESIGN-EXPERT Plot sm oothness R e s id ua ls vs . P re d ic te d -5 2 .5 -2 4 . 6 2 5 3 . 2 5 3 1 .1 2 5 5 9 5 9

R e s id u a l

3 1 . 1 2 5 s l a u d

i 3 . 2 5 s e R

-2 4 . 6 2 5

-5 2 . 5

4 5 .0 0 9 3 .9 1 1 4 2 . 8 1 1 9 1 .7 2 2 4 0 . 6 3 18

P re d i c te d DESIGN-EXPERT Plot sm oothness R e s id ua ls vs . R un 5 9

3 1 . 1 2 5 s l a u d

i 3 . 2 5 s e R

-2 4 . 6 2 5

-5 2 . 5

DESIGN-EXPERT Plot sm oothness 1 R e s4 id ua ls7 vs . 1F 0 e e d1 3ra te 1 6 5 9 R u n N u m b e r

3 1 . 1 2 5 s l a u d

i 3 . 2 5 s e R

-2 4 . 6 2 5

-5 2 . 5

1 0 1 5 2 0 2 5 3 0 3 5 4 0 19

F e e d ra te DESIGN-EXPERT Plot sm oothness R e s id ua ls vs . s p ind le s p e e d 5 9

3 1 . 1 2 5 s l a u d

i 3 . 2 5 s e R

-2 4 . 6 2 5

-5 2 . 5 DESIGN-EXPERT Plot Inte ra c tio n G ra p h 1 0 0 0 1 2 5B 0 : s1 5p 0 in 0 d1 le 7 5s 0 p e2e 0 0d 0 2 2 5 0 2 5 0 0 sm oothness 2 7 9 X = A: Feed rate Y = B: spindle speed s p i n d l e s p e e d

Design Points 2 1 3 . 5 8 2 B- 1000.000

B+ 2500.000 s s e n h 1 4 8t . 1 6 3 o o m s

8 2 . 7 4 5 1

1 7 . 3 2 6 8

1 0 .0 0 1 7 .5 0 2 5 .0 0 3 2 . 5 0 4 0 . 0 0 20

A: F e e d ra te DESIGN-EXPERT Plot

sm oothness X = A: Feed rate Y = B: spindle speed

2 4 0 .6 2 5 1 9 1 .7 1 9

1 4 2.8 1 3 s s

9 3 .9e 0 6 3 n h t

o 4 5 o m s

2 5 0 0 .0 0 4 0 .0 0 2 1 2 5 .0 0 DESIGN-EXPERT Plot 4 s m o o thne s s 4 2 5 0 0 .0 0 3 2 .5 0 1 7 5 0 .0 0 sm oothness 2 5 .0 0 X = A: Feed rate Y = B: spindle speed B : s p in d le s1 p 3 e 7 e 5 .0d 0 1 7 .5 0 A: F e e d ra te 1 0 0 0 .0 0 1 0 .0 0 Design Points 2 1 2 5 .0 0

d 7 7 .6 0 4 2 e e

p 1 1 0 .2 0 8

s 1 4 2 .8 1 3

e 1 7 5l 0 .0 0 d n i p s

: 1 7 5 .4 1 7 B

1 3 7 5 .0 0 2 0 8 .0 2 1

4 4 1 0 0 0 .0 0 1 0 .0 0 1 7 .5 0 2 5 .0 0 3 2 .5 0 4 0 .0 0 21

A: F e e d ra te Works Cited

1. Montgomery, Douglas C. Design and Analysis of Experiments 5th Edition John Wiley & Sons, Inc. New York © 1997, 2001 2. Duff, Larry Integrated Manufacturing Engineering Laboratory Personnel, Arizona State University, Tempe, AZ